TVL1 Shape Approximation from Scattered 3D Data

Eugen Funk, Laurence S. Dooley, Anko Boerner


With the emergence in 3D sensors such as laser scanners and 3D cameras, large 3D point clouds can now be sampled from physical objects within a scene. The raw 3D samples delivered by these sensors however, do not contain any information about the environment the objects exist in, which means that further geometrical high-level modelling is essential. In addition, issues like sparse data measurements, noise, missing samples due to occlusion, and the inherently huge datasets involved in such representations makes this task extremely challenging. This paper addresses these issues by presenting a new 3D shape modelling framework for samples acquired from 3D sensor. Motivated by the success of nonlinear kernel-based approximation techniques in the statistics domain, existing methods using radial basis functions are applied to 3D object shape approximation. The task is framed as an optimization problem and is extended using non-smooth L1 total variation regularization. Appropriate convex energy functionals are constructed and solved by applying the Alternating Direction Method of Multipliers approach, which is then extended using Gauss-Seidel iterations. This significantly lowers the computational complexity involved in generating 3D shape from 3D samples, while both numerical and qualitative analysis confirms the superior shape modelling performance of this new framework compared with existing 3D shape reconstruction techniques.


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Paper Citation

in Harvard Style

Funk E., Dooley L. and Boerner A. (2015). TVL1 Shape Approximation from Scattered 3D Data . In Proceedings of the 10th International Conference on Computer Vision Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2015) ISBN 978-989-758-091-8, pages 294-304. DOI: 10.5220/0005301802940304

in Bibtex Style

author={Eugen Funk and Laurence S. Dooley and Anko Boerner},
title={TVL1 Shape Approximation from Scattered 3D Data},
booktitle={Proceedings of the 10th International Conference on Computer Vision Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2015)},

in EndNote Style

JO - Proceedings of the 10th International Conference on Computer Vision Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2015)
TI - TVL1 Shape Approximation from Scattered 3D Data
SN - 978-989-758-091-8
AU - Funk E.
AU - Dooley L.
AU - Boerner A.
PY - 2015
SP - 294
EP - 304
DO - 10.5220/0005301802940304